3.3 systems of inequalities 2010 - poudre school district 2/c… · 3.3 systems of inequalities...

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3.3 Systems of Inequalities 2010 1 October 20, 2010 Sand 3.3 Systems of Inequalities How do you solve systems of inequalities graphically? What is a solution region? Objective: To solve systems of linear inequalities.

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Page 1: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

1

October 20, 2010

Sand

3.3 Systems of Inequalities

How do you solve systems of inequalities graphically?

What is a solution region?

Objective:  To solve systems of linear inequalities.

Page 2: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

2

October 20, 2010

Oct 2­12:39 PM

Check Skills You'll Need:

Solve each inequality.

1.  5x ­ 6 > 27 2.  ­18 ­ 5y > 52 3.  ­5(4x + 1) < 23

Page 3: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

3

October 20, 2010

Oct 2­12:45 PM

Check Skills You'll Need:  Graph each inequality.

4.  y < 4x ­ 1 5.  3y > 6x + 3 6.  ­5y + 2x > ­5

7.  y < |x| 8.  y > |x + 3| 9.  y < |x ­ 2| + 4

Page 4: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

4

October 20, 2010

Nov 20­6:49 AM

Solving Systems of Linear Equations

To solve a system of linear equations by graphing:Graph each line and find the point of intersection

To solve means:To find a solution that fits both lines.The point of intersection is the only solution that exists where a solution fits both lines.

Recall...

Page 5: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

5

October 20, 2010

Sand

What is a system of inequalities?

y < 2x + 1y < ­2x +5y > ­3{

The shaded region is called the... SOLUTION REGION!

Page 6: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

6

October 20, 2010

Oct 2­12:58 PM

Solve the system of inequalities by graphing.

     x ­ 2y < 6     y < ­3/2x + 5{

Page 7: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

7

October 20, 2010

XY axis ­ large

Solve the system of inequalities.

y > ­x + 42x ­ y > ­2{

Page 8: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

8

October 20, 2010

Oct 2­1:12 PM

Solve the system of inequalities.y < 4y > |x ­ 3|{

Page 9: 3.3 Systems of Inequalities 2010 - Poudre School District 2/C… · 3.3 Systems of Inequalities 2010 4 October 20, 2010 Nov 206:49 AM Solving Systems of Linear Equations To solve

3.3 Systems of Inequalities 2010 

9

October 20, 2010

Sand

Homeworkp136 (4 ­ 38)even